The purpose of our paper is to prove a large deviation principle on the asymptotic behavior of the stochastic differential equations on the sphere S associated with a critical Sobolev Brownian vector field which was constructed by Fang and Zhang 1 . Recall that Schilder theorem states that if B is the real Brownian motion and C0 0, 1 is the space of real continuous functions defined on 0, 1 , n...

A C-linear map θ (not necessarily bounded) between two Hilbert C-modules is said to be ‘orthogonality preserving’ if 〈θ(x), θ(y)〉 = 0 whenever 〈x, y〉 = 0. We prove that if θ is an orthogonality preserving map from a full Hilbert C0()-module E into another Hilbert C0()-module F that satisfies a weaker notion of C0()-linearity (called ‘localness’), then θ is bounded and there exists φ ∈ Cb()+...

(1b) Question. For which pairs (C0,H) does a lift exist? Note that the lifting problem for C0 is formally smooth. However we will see that in general the lifting problem for (C0,H) can be obstructed; in some cases a lifting does not exist, in several cases ramification in R is needed to make a lifting possible. In order to have a positive answer to this question it suffices to consider the case...

A parameter c0?C in the family of quadratic polynomials fc(z)=z2+c is a critical point period n multiplier, if map fc0 has periodic orbit n, whose viewed as locally analytic function c, vanishing derivative at c=c0. We prove that all points multipliers equidistribute on boundary Mandelbrot set, n??.

Sequential estimation of a probability p by means of inverse binomial sampling is considered. For μ1, μ2 > 1 given, the accuracy of an estimator p̂ is measured by the confidence level Pr[p/μ2 ≤ p̂ ≤ pμ1]. The confidence levels c0 that can be guaranteed for p unknown, i.e. such that Pr[p/μ2 ≤ p̂ ≤ pμ1] ≥ c0 for all p ∈ (0, 1), are investigated. It is shown that, within the general class of randomiz...

Let p(x) be a generically stable type over C0, thought of as a C0-definable type over U. The type p(x) might live in an imaginary sort. We are going to prove that there is a small set C ⊇ C0 and a C-definable map f into a power of k such that p is “dominated” over C by its pushforward along f . That is, for every D ⊇ C and every a, the following will be equivalent: • a |= p|D • a |= p|C and f(a...

Here, we propose new algorithm for solving ECDLP named ”Bit Coincidence Mining Algorithm!”, from which ECDLP is reduced to solving some quadratic equations system. In this algorithm, ECDLP of an elliptic curve E defined over Fq (q is prime or power of primes) reduces to solving quadratic equations system of d − 1 variables and d+C0−1 equations where C0 is small natural number and d ∼ C0 log2 q....

Cash-flow Notation: We use (c0, c1, . . . , ci, . . . , cn) to denote the series of cash-flows where ci is received at time t = i . The length of a period, i.e. the interval of time between t = i and t = i + 1, will usually be understood from the context. Negative cash-flows refer to cash payments. The initial cash-flow, c0, will often be negative while the remaining cash-flows are positive. Th...

We generalize results concerning C0-semigroups on Banach lattices to a setting of ordered Banach spaces. We prove that the generator of a disjointness preserving C0-semigroup is local. Some basic properties of local operators are also given. We investigate cases where local operators generate local C0-semigroups, by using Taylor series or Yosida approximations. As norms we consider regular norm...

Let Z ⊂ Pr be a smooth variety of dimension n and let c0, . . . , cn be the Chern classes of Z. We present an algorithm to compute the degree of any monomial in {c0, . . . , cn}. The method is based on intersection theory and may be implemented as a numeric or as a symbolic algorithm.